Solve for $x$: $\frac{6x^2 + 111x +1}{2x+37} = 3x + 1$.
Answer: Multiplying both sides by $2x+37$ gives  \begin{align*}
6x^2 + 111x + 1 &= (2x+37)(3x+1)\\
&=2x(3x+1) + 37(3x+1)\\
&= 6x^2 + 2x + 111x + 37\\
&= 6x^2 +113x + 37
\end{align*}So, we have \[6x^2 + 111x + 1 = 6x^2+ 113x + 37.\]Subtracting $6x^2$ from both sides gives $111x+1 = 113x + 37$.  Rearranging this equation gives $2x = -36$, from which we find $x = \boxed{-18}$.